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In this thesis, the first on-line mass measurements of the isotopes 52,53K have been performed. These measurements by multi-reflection time-of-flight mass spectrometry with the ISOLTRAP setup at ISOLDE/CERN are linked to previously measured masses of exotic Ca isotopes, which had shown an unexpected large neutron-shell gap at the neutron number N = 32 for the magic proton core Z = 20. The new measurements provide the first exploration of the N = 32 neutron-shell closure below the proton number Z = 20. With a measured empirical two-neutron shell gap of about 3MeV for 51K, the N = 32 gap is smaller as compared to that of 52Ca, which measures about 4MeV, but is still significantly present. This confirms that the nuclear shell effect measured for calcium isotopes is not a phenomenon purely raised by its closed-proton-shell configuration, but is also present in potassium isotopes that possess an open proton shell and an unpaired proton. The second main objective of this thesis was the development of new techniques for efficient mass separation in Penning traps and multi-reflection devices, because the success of nuclear mass measurements with high precision depends crucially on the purity of the ion ensemble. The two main difficulties that have been addressed are, first, when the masses of the ions of interest and the masses of contaminant ions are very similar, and second, when the contaminant ions are predominantly present in the beam from ISOLDE. For the removal of contaminant ions in a high-vacuum Penning trap with high resolving power, a new technique for mass separation has been developed. A simultaneous application of a dipolar radio-frequency field at the magnetron frequency of all ions (mass independent at leading order) and a quadrupolar radio-frequency field at the cyclotron frequency (highly mass dependent) of a chosen ion species provides a new way of ion purification. The result is that the magnetron radius of all ions is increased by the effect of the dipolar excitation, and, at the same time, the quadrupolar excitation leads to a conversion of the radial eigenmotions for the chosen species. The consequence of this simultaneous process is that the wanted ions move back to the trap axes while all other ions are radially ejected from the trap. The advantage of the new method is the simultaneous ejection of all unwanted species in a high vacuum, which otherwise have to be addressed by a dipolar excitation at different frequencies, or by use of complex waveforms if a broadband ejection is required. A comparable (general) broadband ejection as achieved by the new method was previously only achieved in buffer-gas filled Penning traps. Further technical developments were performed with ISOLTRAPâ€™s multi-reflection time-of-flight mass separator. The goal was to improve on situations when dealing with highly contaminated beams from ISOLDE during on-line Penning-trap measurements. In such cases, the number of events obtained in a limited time can be very low for the reason that only a limited number of ions, which predominantly consist of contaminant ions, can be stored and separated in the multi-reflection device at a given time to avoid non-negligible Coulomb interactions between the ions. The situation at ISOLTRAP has been significantly improved by a more efficient use of the separation cycle of the multi-reflection device. The mass-separation cycle is by far shorter (on the order of 10 ms) than a Penning-trap mass measurement (on the order of seconds). Thus, the separation in the multi-reflection device has been decoupled from the Penning-trap mass measurement and is repeated rapidly, while the purified ions are accumulated, stored, and cooled in the preparation Penning trap of ISOLTRAP. The collected ions of interest can then be transferred to the precision-measurement trap. This method increases the possible ratio of the number of contaminant ions to ions of interest by up to two orders of magnitude, i.e. the ratio of the corresponding process durations. Additionally, space-charge problems in multi-reflection devices have been investigated by setting up an off-line apparatus at Greifswald. The dynamical effects of ions in multi-reflection devices under non-negligible Coulomb interactions have been investigated in order to search for possibilities for improvements on such situations. This resulted in a new method of manipulating the ion densities in the device. The ions move in a cloud with large spatial extend for the major part of the trapping time and can later be compressed to small bunches for high-resolution mass separation. Proof-of-principle measurement have been performed with a low number of stored ions, where successful isobar separation has been demonstrated.